The invention relates to the detection and resolution of multiple targets (or energy sources) from signals obtained by a spatial array of sensors. The invention has wide application in such diverse fields as passive sonar, in which case the sensors would be acoustic and the targets might be hostile submarines, earthquake and nuclear weapon detonation detection systems, in which case the sensors would be seismic and the targets the earthquake or explosion epicenters, astronomical interferometry wherein the sensors would be radiotelescopes and the targets may be distant galaxies or quasars, and phased-array radars in which case the sensors would be the array antennae. More particularly, the invention is intended to be used for precision target detection of enemy targets to enable a strike on said enemies to be commanded electronically by a battlefield command control center.
When a signal is known to consist of pure sinusoids in white noise, an appropriate procedure for determining the unknown frequencies and powers is the Pisarenko spectral-decomposition described in his paper entitled "The Retrieval of Harmonics from a Co-Variance Function", Geophysical Journal of the Royal Astronomical Society, Vol. 33, pp 347-366, 1973. All that is needed is a finite segment of the discrete covariance function whose length is at least one more than the number of sinusoids to be determined. The method is based on eigenanalysis of a Toeplitz matrix produced from the covariance function.
When Pisarenko extended this method to signals where the amplitudes and the frequencies have small random perturbations around central values he showed that linear approximation is justified when the number of sinusoids is one less than the number of eigenvectors. However, when a larger segment of the covariance function was used, leading to a larger number of eigenvectors, the statistical analysis was much more difficult. These extra eigenvectors also produced false sinusoids which appeared at fictitious frequencies with fictitious amplitudes. As a result he recommended disregarding the extra covariance data.
Since then the extension of the Pisarenko method to the problem of extracting multiple-target information from array data has led to many different techniques, e.g., the Eigen-Vector Method EVM, of Johnson and Degraff, see IEEE trans. on ASSP, Vol. 30, pp 638-647, August 1982 and the Multiple-Signal-Classification scheme (MUSIC) of Schmidt, see Proceedings RADC Sprectral Estimation Workshop, Rome, N.Y., pp. 243-258, October 1979. Between the desire to use all the available information and the problem of coping with false alarms, investigators adopted the concept of artificially dividing the eigenspace of the signal covariance matrix into two subspaces, (1) the source space, consisting of eigenvectors with large eigenvalues, and (2) noise space, consisting of the remaining eigenvectors. In these approaches the distinction between the two spaces requires a subjective judgment (or guess) on the dividing line between the sets of eigenvalues. In any case, it must be recognized that any such distinction is artificial since the noise occupies all of the eigenspace, and each eigenvector may have contributions from any source.
In these prior art procedures a metric is then formed from the so-called noise space to measure its deviation from orthogonality to the true source space. The inverse of this metric is then used to indicate the directions of arrival and the powers of the various sources. The effect of using several eigenvectors in the metric tends to decrease the number of false alarms and to produce an average location for each source. Each investigator pursuing this approach used some kind of metric, but none of them proved that the resulting procedures led to "optimum" target resolution in any sense. The present invention comprises a different approach which while based on the Pisarenko method, differs from the earlier ad hoc approaches and yields demonstrably better multi-target resolution.